2019/10/25 by Umar Islambekov, Islambekov, Umar, Yulia R. Gel +1
Computer Science · #Algebraic Topology (math.AT) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1910.11525
openalex publication_date 2019/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic topology used to extract topological information from data - in unsupervised learning is an uncommon and a novel approach. A notable aspect of this methodology consists in analyzing data at multiple resolutions which allows to distinguish true features from noise based on the extent of their persistence. We evaluate the performance of our algorithm on synthetic data and compare it to other well-known clustering algorithms such as K-means, hierarchical clustering and DBSCAN. We illustrate its application in the context of a case study of water quality in the Chesapeake Bay.